OFFSET
1,2
COMMENTS
The modulus k=3-2*sqrt(2).
K(k_4) in the Mathworld link.
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Elliptic Integral Singular Values
I. J. Zucker and G. S. Joyce, Special values of the hypergeometric series II, Math. Proc. Camb. Phil. Soc. 131 (2001) 309-319. Table 1 N=4.
FORMULA
Equals 2*(2+sqrt(2))*Pi^(3/2)/Gamma(-1/4)^2.
EXAMPLE
1.58255172722371591183313507107040987652948814961878924349716944847...
MAPLE
evalf(2*(2+sqrt(2))*Pi^(3/2)/GAMMA(-1/4)^2, 120); # Muniru A Asiru, Oct 08 2018
MATHEMATICA
RealDigits[N[EllipticK[(3 - 2 Sqrt[2])^2], 105]][[1]]
RealDigits[2*(2+Sqrt[2])*Pi^(3/2)/Gamma[-1/4]^2, 10, 100][[1]] (* G. C. Greubel, Oct 08 2018 *)
PROG
(PARI) default(realprecision, 100); 2*(2+sqrt(2))*Pi^(3/2)/gamma(-1/4)^2 \\ G. C. Greubel, Oct 08 2018
(Magma) SetDefaultRealField(RealField(100)); R:= RealField(); 2*(2+Sqrt(2))*Pi(R)^(3/2)/Gamma(-1/4)^2; // G. C. Greubel, Oct 08 2018
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Benedict W. J. Irwin, Sep 07 2016
STATUS
approved